Connectedness locus

In one-dimensional complex dynamics, the connectedness locus is a subset of the parameter space of rational functions, which consists of those parameters for which the corresponding Julia set is connected. In one-dimensional complex dynamics, the connectedness locus is a subset of the parameter space of rational functions, which consists of those parameters for which the corresponding Julia set is connected. Without doubt, the most famous connectedness locus is the Mandelbrot set, which arises from the family of complex quadratic polynomials :